CBSE Class 12-science Answered

solve the following system of equation by matrix method

1)x+y+z=6,x-y-z=-4,x+2y-2z=-1

2)x-y+3z=10,x-y-z=-2,2x+3y+4z=4

3)x+y+z=6,x-2y+3z=6,x-y+z=2

4)2x+y+2z=5,x-y-z=0,x+2y+3z=5

5)x+2y+3z=2,2x+3y+z=-1,x-y-z=-2

Asked by geethapai2004 | 19 Apr, 2016, 09:35: PM

Expert Answer

left parenthesis 1 right parenthesis C o n s i d e r space t h e space g i v e n space s y s t e m space o f space e q u a t i o n s colon x plus y plus z equals 6 x minus y minus z equals negative 4 x plus 2 y minus 2 z equals negative 1 L e t space u s space w r i t e space t h e space a b o v e space s y s t e m space o f space e q u a t i o n s space a s colon open square brackets table row 1 1 1 row 1 cell negative 1 end cell cell negative 1 end cell row 1 2 cell negative 2 end cell end table close square brackets open square brackets table row x row y row z end table close square brackets equals open square brackets table row 6 row cell negative 4 end cell row cell negative 1 end cell end table close square brackets A X equals B comma space w h e r e comma space A equals open square brackets table row 1 1 1 row 1 cell negative 1 end cell cell negative 1 end cell row 1 2 cell negative 2 end cell end table close square brackets comma space X equals open square brackets table row x row y row z end table close square brackets space a n d space B equals open square brackets table row 6 row cell negative 4 end cell row cell negative 1 end cell end table close square brackets L e t space u s space m u l t i p l y comma space A to the power of negative 1 end exponent space o n space b o t h space t h e space s i d e s comma space w e space h a v e comma A to the power of negative 1 end exponent A X equals A to the power of negative 1 end exponent B rightwards double arrow I X equals A to the power of negative 1 end exponent B rightwards double arrow X equals A to the power of negative 1 end exponent B C o n s i d e r space t h e space g i v e n space m a t r i x space A space a n d space w e space n e e d space t o space f i n d space A to the power of negative 1 end exponent colon W e space k n o w space t h a t comma space A equals I A open square brackets table row 1 1 1 row 1 cell negative 1 end cell cell negative 1 end cell row 1 2 cell negative 2 end cell end table close square brackets equals open square brackets table row 1 0 0 row 0 1 0 row 0 0 1 end table close square brackets A A p p l y i n g space R subscript 2 rightwards arrow R subscript 2 minus R subscript 1 space a n d space R subscript 3 rightwards arrow R subscript 3 minus R subscript 1 comma space w e space h a v e comma open square brackets table row 1 1 1 row 0 cell negative 2 end cell cell negative 2 end cell row 0 1 cell negative 3 end cell end table close square brackets equals open square brackets table row 1 0 0 row cell negative 1 end cell 1 0 row cell negative 1 end cell 0 1 end table close square brackets A A p p l y i n g space R subscript 3 rightwards arrow 2 R subscript 3 plus R subscript 2 comma space w e space h a v e comma open square brackets table row 1 1 1 row 0 cell negative 2 end cell cell negative 2 end cell row 0 0 cell negative 8 end cell end table close square brackets equals open square brackets table row 1 0 0 row cell negative 1 end cell 1 0 row cell negative 3 end cell 1 2 end table close square brackets A A p p l y i n g space R subscript 3 rightwards arrow fraction numerator R subscript 3 over denominator negative 8 end fraction comma space w e space h a v e comma open square brackets table row 1 1 1 row 0 cell negative 2 end cell cell negative 2 end cell row 0 0 1 end table close square brackets equals open square brackets table row 1 0 0 row cell negative 1 end cell 1 0 row cell 3 over 8 end cell cell fraction numerator negative 1 over denominator 8 end fraction end cell cell fraction numerator negative 2 over denominator 8 end fraction end cell end table close square brackets A A p p l y i n g space R subscript 2 rightwards arrow fraction numerator R subscript 2 over denominator negative 2 end fraction comma space w e space h a v e comma open square brackets table row 1 1 1 row 0 1 1 row 0 0 1 end table close square brackets equals open square brackets table row 1 0 0 row cell 1 half end cell cell fraction numerator negative 1 over denominator 2 end fraction end cell 0 row cell 3 over 8 end cell cell fraction numerator negative 1 over denominator 8 end fraction end cell cell fraction numerator negative 2 over denominator 8 end fraction end cell end table close square brackets A A p p l y i n g space R subscript 2 rightwards arrow R subscript 2 minus R subscript 3 comma space w e space h a v e comma open square brackets table row 1 1 1 row 0 1 0 row 0 0 1 end table close square brackets equals open square brackets table row 1 0 0 row cell 1 over 8 end cell cell fraction numerator negative 3 over denominator 8 end fraction end cell cell 2 over 8 end cell row cell 3 over 8 end cell cell fraction numerator negative 1 over denominator 8 end fraction end cell cell fraction numerator negative 2 over denominator 8 end fraction end cell end table close square brackets A A p p l y i n g space R subscript 1 rightwards arrow R subscript 1 minus R subscript 2 comma space w e space h a v e comma open square brackets table row 1 0 1 row 0 1 0 row 0 0 1 end table close square brackets equals open square brackets table row cell 7 over 8 end cell cell 3 over 8 end cell cell fraction numerator negative 2 over denominator 8 end fraction end cell row cell 1 over 8 end cell cell fraction numerator negative 3 over denominator 8 end fraction end cell cell 2 over 8 end cell row cell 3 over 8 end cell cell fraction numerator negative 1 over denominator 8 end fraction end cell cell fraction numerator negative 2 over denominator 8 end fraction end cell end table close square brackets A A p p l y i n g space R subscript 1 rightwards arrow R subscript 1 minus R subscript 3 comma space w e space h a v e comma open square brackets table row 1 0 0 row 0 1 0 row 0 0 1 end table close square brackets equals open square brackets table row cell 4 over 8 end cell cell 4 over 8 end cell 0 row cell 1 over 8 end cell cell fraction numerator negative 3 over denominator 8 end fraction end cell cell 2 over 8 end cell row cell 3 over 8 end cell cell fraction numerator negative 1 over denominator 8 end fraction end cell cell fraction numerator negative 2 over denominator 8 end fraction end cell end table close square brackets A T h u s comma space A to the power of negative 1 end exponent equals open square brackets table row cell 4 over 8 end cell cell 4 over 8 end cell 0 row cell 1 over 8 end cell cell fraction numerator negative 3 over denominator 8 end fraction end cell cell 2 over 8 end cell row cell 3 over 8 end cell cell fraction numerator negative 1 over denominator 8 end fraction end cell cell fraction numerator negative 2 over denominator 8 end fraction end cell end table close square brackets W e space h a v e comma space X equals A to the power of negative 1 end exponent B T h u s comma space open square brackets table row x row y row z end table close square brackets equals open square brackets table row cell 4 over 8 end cell cell 4 over 8 end cell 0 row cell 1 over 8 end cell cell fraction numerator negative 3 over denominator 8 end fraction end cell cell 2 over 8 end cell row cell 3 over 8 end cell cell fraction numerator negative 1 over denominator 8 end fraction end cell cell fraction numerator negative 2 over denominator 8 end fraction end cell end table close square brackets open square brackets table row 6 row cell negative 4 end cell row cell negative 1 end cell end table close square brackets rightwards double arrow open square brackets table row x row y row z end table close square brackets equals open square brackets table row cell 4 over 8 end cell cell 4 over 8 end cell 0 row cell 1 over 8 end cell cell fraction numerator negative 3 over denominator 8 end fraction end cell cell 2 over 8 end cell row cell 3 over 8 end cell cell fraction numerator negative 1 over denominator 8 end fraction end cell cell fraction numerator negative 2 over denominator 8 end fraction end cell end table close square brackets open square brackets table row 6 row cell negative 4 end cell row cell negative 1 end cell end table close square brackets rightwards double arrow open square brackets table row x row y row z end table close square brackets equals open square brackets table row 1 row 2 row 3 end table close square brackets T h u s comma space x equals 1 comma space y equals 2 space a n d space z equals 3

Answered by Vimala | 20 Apr, 2016, 10:57: AM

CBSE Class 12-science Answered

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CBSE Class 12-science Answered

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